Until very recently, it had been considered that the vanishing of the Luttinger integrals represents one of the
hallmarks of Fermi liquid phases [1]}, [2]}.
In this way, the (ordinary) Friedel sum rules state that the quasiparticle phase shifts are simply the impurity occupancies divided by \(\pi ,\) 
as it was known from the fifties.
However, in the last two years, it was shown that, for certain single-impurity [3]}, [4]} and two-impurity [5]}, [6]} models,
the Luttinger integrals can take the discrete values \(\pm \pi /2\)  in the so-called non-Landau Fermi liquids (NLFL), that is, Fermi liquid phases
that are not adiabatically connected with their non-interacting counterparts [3]}.
In this work we have found that an iron phthalocyanine molecule on Au(111) behaves as a NLFL in the absence of an applied magnetic field, while for \(B \ne 0\) 
it is an “ordinary” Fermi liquid, but with non-zero Luttinger integrals that change continuosly with \(B\) .
So, we have shown that there are Fermi liquids in which the Friedel sum rules (REF ) holds only in its
generalized version with non-zero (continuous)
Luttinger integrals.
